How Is the Man's Mass Calculated from Throwing a Ball on Ice?

[davedays]

Homework Statement

A man is standing on a frozen pond (which is mean less).
He throws a ball m=250 g
The speed of the ball is 8.0 ms^-1
The man moves back at a speed of 0.05 ms^-1
How heavy is the man ?

Homework Equations

p1=p2
m1 x v1 = m2 x v2

The Attempt at a Solution

p1=p2
m1 v1 = m2 v2

250 x 8 = m2 x 0.05
2000 = 0.05 m2
m2= 40000 [g] = 40 [kg]

is this correct ?


Thanks,
dave

 

[Cryphonus]

Correct.

 

[kerimek]

Yes, your solution is correct. The man's mass is indeed 40 kg. This can be confirmed by using the equation for momentum, which states that the total momentum of a system is conserved. In this case, the initial momentum of the system (man and ball) is equal to the final momentum of the system.

Initial momentum = m1 x v1 = (0.25 kg)(8 m/s) = 2 kg m/s
Final momentum = m2 x v2 = (40 kg)(0.05 m/s) = 2 kg m/s

Therefore, the man's mass is indeed 40 kg. This also makes sense intuitively, as the man's movement is much slower compared to the ball's, so his mass must be much larger in order for the total momentum to be conserved.